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A general result on almost sure central limit theorem for self-normalized sums for mixing sequences*

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Abstract

Let X, X 1 , X 2 , . . . be a sequence of strictly stationary ϕ-mixing random variables with zero means. In this paper, we show that a self-normalized version of almost sure central limit theorem holds under the assumptions that the mixing coefficients satisfy \( \sum\nolimits_{n=1}^{\infty } {{\phi^{{{1 \left/ {2} \right.}}}}\left( {{2^n}} \right)<\infty } \); moreover, we no longer restrict ourselves to logarithmic averages, but allow rather arbitrary weight sequences.

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Authors and Affiliations

  1. College of Mathematics, Jilin University, Changchun, 130012, PR China

    Yong Zhang

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  1. Yong Zhang
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Correspondence to Yong Zhang.

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* The research was supported by the Basic Research Foundation of Jilin University (grant No. 201103204), the National Natural Science Foundation of China (grant No. 11101180), and the Science and Technology Development Program of Jilin Province (grant No. 20130522096JH).

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Zhang, Y. A general result on almost sure central limit theorem for self-normalized sums for mixing sequences* . Lith Math J 53, 471–483 (2013). https://doi.org/10.1007/s10986-013-9222-8

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  • DOI: https://doi.org/10.1007/s10986-013-9222-8

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